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Article: Nonlinear Poisson - Boltzmann equation in a model of a scanning tunneling microscope
Title | Nonlinear Poisson - Boltzmann equation in a model of a scanning tunneling microscope |
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Authors | |
Issue Date | 1994 |
Publisher | John Wiley & Sons, Inc. The Journal's web site is located at http://www.interscience.wiley.com/jpages/0749-159X/ |
Citation | Numerical Methods For Partial Differential Equations, 1994, v. 10 n. 6, p. 689-702 How to Cite? |
Abstract | The nonlinear Poisson - Boltzmann equation is solved in the region between a sphere and a plane, which models the electrolyte solution interface between the tip and the substrate in a scanning tunneling microscope. A finite difference method is used with the domain transformed into bispherical coordinates. Picard iteration with relaxation is used to achieve convergence for this highly nonlinear problem. An adsorbed molecule on the substrate can also be modelled by a superposition of a perturbing potential in a small region of the plane. An approximate analytical solution using a superposition of individual solutions for plane, the adsorbed molecule, and the sphere is also attempted. Results for cases of different potential values on the boundary surfaces and different distances of the sphere from the plane are presented. The results of the numerical method, the approximate analytical method, as well as the previous solutions of the linearized equation are compared. |
Persistent Identifier | http://hdl.handle.net/10722/167526 |
ISSN | 2023 Impact Factor: 2.1 2023 SCImago Journal Rankings: 0.979 |
DC Field | Value | Language |
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dc.contributor.author | Chan, KwongYu | en_US |
dc.contributor.author | Henderson, Douglas | en_US |
dc.contributor.author | Stenger, Frank | en_US |
dc.date.accessioned | 2012-10-08T03:08:04Z | - |
dc.date.available | 2012-10-08T03:08:04Z | - |
dc.date.issued | 1994 | en_US |
dc.identifier.citation | Numerical Methods For Partial Differential Equations, 1994, v. 10 n. 6, p. 689-702 | en_US |
dc.identifier.issn | 0749-159X | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/167526 | - |
dc.description.abstract | The nonlinear Poisson - Boltzmann equation is solved in the region between a sphere and a plane, which models the electrolyte solution interface between the tip and the substrate in a scanning tunneling microscope. A finite difference method is used with the domain transformed into bispherical coordinates. Picard iteration with relaxation is used to achieve convergence for this highly nonlinear problem. An adsorbed molecule on the substrate can also be modelled by a superposition of a perturbing potential in a small region of the plane. An approximate analytical solution using a superposition of individual solutions for plane, the adsorbed molecule, and the sphere is also attempted. Results for cases of different potential values on the boundary surfaces and different distances of the sphere from the plane are presented. The results of the numerical method, the approximate analytical method, as well as the previous solutions of the linearized equation are compared. | en_US |
dc.language | eng | en_US |
dc.publisher | John Wiley & Sons, Inc. The Journal's web site is located at http://www.interscience.wiley.com/jpages/0749-159X/ | en_US |
dc.relation.ispartof | Numerical Methods for Partial Differential Equations | en_US |
dc.title | Nonlinear Poisson - Boltzmann equation in a model of a scanning tunneling microscope | en_US |
dc.type | Article | en_US |
dc.identifier.email | Chan, KwongYu:hrsccky@hku.hk | en_US |
dc.identifier.authority | Chan, KwongYu=rp00662 | en_US |
dc.description.nature | link_to_subscribed_fulltext | en_US |
dc.identifier.doi | 10.1002/num.1690100605 | - |
dc.identifier.scopus | eid_2-s2.0-0028545510 | en_US |
dc.identifier.volume | 10 | en_US |
dc.identifier.issue | 6 | en_US |
dc.identifier.spage | 689 | en_US |
dc.identifier.epage | 702 | en_US |
dc.publisher.place | United States | en_US |
dc.identifier.scopusauthorid | Chan, KwongYu=7406034142 | en_US |
dc.identifier.scopusauthorid | Henderson, Douglas=7402988756 | en_US |
dc.identifier.scopusauthorid | Stenger, Frank=7003354565 | en_US |
dc.identifier.issnl | 0749-159X | - |